@. V. Trinité, N. Vast, M. Hayoun, H. Dammak, and J. C. , Tolédano lettre en préparation Phase stability in titanium ? L.Dash, Vast and L. Reining, disponible en ligne dans Comp. Mat. Sci. (1006) Electronic excitations : ab initio calculations of electronic spectra and application to zirconia ZrO 2 titania TiO 2 and cuprous oxide Cu 2 O

@. V. Trinité, N. Vast, and M. , Hayoun en préparation Self-interaction corrected pseudopotentials for semicore states in tita- nium ? V. Trinité, Vast, M. Hayoun en préparation Effect of the semicore states in pseudopotentials for transition metals

@. V. Trinité, N. Vast, M. Hayoun, and H. , Dammak à prévoir Elastic constants within DFT : method and application to titanium ? V. Trinité

]. R. Ahuja, J. Wills, B. Johansson, and O. Eriksson, Crystal structures of Ti, Zr, and Hf under compression: Theory, Physical Review B, vol.48, issue.22, p.16269, 1993.
DOI : 10.1103/PhysRevB.48.16269

]. J. Perdew and A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Physical Review B, vol.23, issue.10, p.5048, 1981.
DOI : 10.1103/PhysRevB.23.5048

]. M. Finnis, A. Paxton, M. Methfessel, and M. Van-schilfgaarde, Crystal Structures of Zirconia from First Principles and Self-Consistent Tight Binding, Physical Review Letters, vol.81, issue.23, p.5149, 1998.
DOI : 10.1103/PhysRevLett.81.5149

P. Hohenberg and W. Kohn, Inhomogeneous Electron Gas, Physical Review, vol.136, issue.3B, p.864, 1964.
DOI : 10.1103/PhysRev.136.B864

W. Kohn and L. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, Physical Review, vol.140, issue.4A, p.1133, 1965.
DOI : 10.1103/PhysRev.140.A1133

R. Dreizler and E. Gross, Density Functional Theory (Spinger-Verlag, 1990.

D. M. Ceperley and B. J. Adler, Ground State of the Electron Gas by a Stochastic Method, Physical Review Letters, vol.45, issue.7, p.566, 1980.
DOI : 10.1103/PhysRevLett.45.566

R. O. Jones and O. Gunnarsson, The density functional formalism, its applications and prospects, Reviews of Modern Physics, vol.61, issue.3, p.689, 1989.
DOI : 10.1103/RevModPhys.61.689

J. Kübler and V. Eyert, Electronic structure calculations dans : Electronic and Magnetic Properties of Metals and Ceramics, 1992.

J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Physical Review Letters, vol.77, issue.18, p.3865, 1996.
DOI : 10.1103/PhysRevLett.77.3865

G. Garcia, C. Elsässer, S. Louie, and M. Cohen, Use of gradient-corrected functionals in total-energy calculations for solids, Physical Review B, vol.46, issue.15, p.9829, 1992.
DOI : 10.1103/PhysRevB.46.9829

A. Zupan, P. Blaha, K. Schwartz, and J. P. Perdew, and Fe: Performance of local-spin-density and generalized-gradient-approximation density functionals, Physical Review B, vol.58, issue.17, p.11266, 1998.
DOI : 10.1103/PhysRevB.58.11266

O. Nielsen and R. M. Martin, First-Principles Calculation of Stress, Physical Review Letters, vol.50, issue.9, p.697, 1983.
DOI : 10.1103/PhysRevLett.50.697

J. Ihm, A. Zunger, and M. Cohen, Momentum-space formalism for the total energy of solids, Journal of Physics C: Solid State Physics, vol.12, issue.21, p.4409, 1979.
DOI : 10.1088/0022-3719/12/21/009

E. Shirley, D. Allan, R. Martin, and J. Joannopoulos, Extended norm-conserving pseudopotentials, Physical Review B, vol.40, issue.6, p.3652, 1989.
DOI : 10.1103/PhysRevB.40.3652

D. Hamann, M. Schlüter, and C. Chiang, Norm-Conserving Pseudopotentials, Physical Review Letters, vol.43, issue.20, p.1494, 1979.
DOI : 10.1103/PhysRevLett.43.1494

D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Physical Review B, vol.41, issue.11, p.7892, 1990.
DOI : 10.1103/PhysRevB.41.7892

S. Louie, S. Froyen, and M. Cohen, Nonlinear ionic pseudopotentials in spin-density-functional calculations, Physical Review B, vol.26, issue.4, p.1738, 1982.
DOI : 10.1103/PhysRevB.26.1738

L. Kleinman and D. Bylander, Efficacious Form for Model Pseudopotentials, Physical Review Letters, vol.48, issue.20, p.1425, 1982.
DOI : 10.1103/PhysRevLett.48.1425

P. Blöchl, Generalized separable potentials for electronic-structure calculations, Physical Review B, vol.41, issue.8, p.5414, 1990.
DOI : 10.1103/PhysRevB.41.5414

P. Blöchl, Projector augmented-wave method, Physical Review B, vol.50, issue.24, p.17953, 1994.
DOI : 10.1103/PhysRevB.50.17953

M. Chou, Reformulation of generalized separable pseudopotentials, Physical Review B, vol.45, issue.20, p.11465, 1992.
DOI : 10.1103/PhysRevB.45.11465

J. Murray and H. Wriedt, Phase Diagrams of Binary Titanium Alloy, 1987.

Y. Vohra and P. Spencer, -Phase of Titanium Metal at Megabar Pressures, Physical Review Letters, vol.86, issue.14, p.3068, 2001.
DOI : 10.1103/PhysRevLett.86.3068

URL : https://hal.archives-ouvertes.fr/hal-00571106

D. Young, Phase Diagrams of the Elements, 1991.
DOI : 10.2172/4010212

Y. Akahama, H. Kawamura, and T. L. Bihan, (Distorted-bcc) Titanium to 220 GPa, Physical Review Letters, vol.87, issue.27, p.275503, 2001.
DOI : 10.1103/PhysRevLett.87.275503

R. Ahuja, L. Dubrovonsky, N. Dubrovinskaia, J. O. Guillen, M. Mattesini et al., calculations, Physical Review B, vol.69, issue.18, p.184102, 2004.
DOI : 10.1103/PhysRevB.69.184102

URL : https://hal.archives-ouvertes.fr/hal-00532121

A. Kutepov and S. Kutepova, Crystal structures of Ti under high pressure: Theory, Physical Review B, vol.67, issue.13, p.132102, 2003.
DOI : 10.1103/PhysRevB.67.132102

D. Trinkle, R. Hennig, S. Srinivasan, D. Hatch, M. Jones et al., Martensitic Transformation in Pure Titanium, Physical Review Letters, vol.91, issue.2, p.25701, 2003.
DOI : 10.1103/PhysRevLett.91.025701

R. Hennig, D. Tinkle, J. Bouchet, S. Srinivasan, R. Albers et al., Impurities block the ?? to ?? martensitic transformation in titanium, Nature Materials, vol.37, issue.2, p.129, 2005.
DOI : 10.1088/0953-8984/6/40/015

S. Rudin, M. Jones, and R. Albers, Thermal stabilization of the hcp phase in titanium, Physical Review B, vol.69, issue.9, p.94117, 2004.
DOI : 10.1103/PhysRevB.69.094117

A. Aguayo, G. Murrieta, and R. De-coss, Elastic stability and electronic structure of fcc Ti, Zr, and Hf: A first-principles study, Physical Review B, vol.65, issue.9, p.92106, 2002.
DOI : 10.1103/PhysRevB.65.092106

S. Nishitani, H. Kawabe, and M. Aoki, First-principles calculations on bcc???hcp transition of titanium, Materials Science and Engineering: A, vol.312, issue.1-2, p.77, 2001.
DOI : 10.1016/S0921-5093(00)01905-5

E. Fisher and C. Renken, Single-Crystal Elastic Moduli and the hcp ??? bcc Transformation in Ti, Zr, and Hf, Physical Review, vol.135, issue.2A, p.482, 1964.
DOI : 10.1103/PhysRev.135.A482

R. Lazzeri, A. Vittadini, and A. Selloni, anatase surfaces, Physical Review B, vol.63, issue.15, p.155409, 2001.
DOI : 10.1103/PhysRevB.63.155409

A. Navrotsky and O. Kleppa, Enthalpy of the Anatase-Rutile Transformation, Journal of the American Ceramic Society, vol.48, issue.584, p.626, 1967.
DOI : 10.1016/0022-5088(66)90074-9

M. Mikami, S. Nakamura, O. Kitao, H. Arakawa, and X. Gonze, First-Principles Study of Titanium Dioxide: Rutile and Anatase, Japanese Journal of Applied Physics, vol.39, issue.Part 2, No. 8B, p.847, 2000.
DOI : 10.1143/JJAP.39.L847

C. Cousins and J. Phys, C : Solid State Phys, 1978.

C. Cousins and J. Phys, C : Solid State Phys, p.989, 1979.

F. Jona and P. Marcus, Structural properties of copper, Physical Review B, vol.63, issue.9, p.94113, 2001.
DOI : 10.1103/PhysRevB.63.094113

F. Jona and P. Marcus, Hexagonal and tetragonal states of magnesium by first principles, Physical Review B, vol.66, issue.9, p.94104, 2002.
DOI : 10.1103/PhysRevB.66.094104

M. Mehl and D. Papaconstantopoulos, Applications of a tight-binding total-energy method for transition and noble metals: Elastic constants, vacancies, and surfaces of monatomic metals, Physical Review B, vol.54, issue.7, p.4519, 1996.
DOI : 10.1103/PhysRevB.54.4519

L. Fast and J. Wills, Elastic constants of hexagonal transition metals: Theory, Physical Review B, vol.51, issue.24, p.17431, 1995.
DOI : 10.1103/PhysRevB.51.17431

C. Bercegeay and S. Bernard, First-principles equations of state and elastic properties of seven metals, Physical Review B, vol.72, issue.21, p.214101, 2005.
DOI : 10.1103/PhysRevB.72.214101

N. Bernstein, H. Gotsis, D. Papaconstantopoulos, and M. Mehl, Tight-binding calculations of the band structure and total energies of the various polytypes of silicon carbide, Physical Review B, vol.71, issue.7, p.75203, 2005.
DOI : 10.1103/PhysRevB.71.075203

S. Baroni, S. De-gironcoli, A. D. Corso, and P. Giannozzi, Phonons and related crystal properties from density-functional perturbation theory, Reviews of Modern Physics, vol.73, issue.2, p.515, 2001.
DOI : 10.1103/RevModPhys.73.515

D. Hamann, X. Wu, K. Rabe, and D. Vanderbilt, Metric tensor formulation of strain in density-functional perturbation theory, Physical Review B, vol.71, issue.3, p.35117, 2005.
DOI : 10.1103/PhysRevB.71.035117

X. Wu, D. Vanderbilt, and D. Hamann, Systematic treatment of displacements, strains, and electric fields in density-functional perturbation theory, Physical Review B, vol.72, issue.3, p.35105, 2005.
DOI : 10.1103/PhysRevB.72.035105

X. Gonze, J. M. Beuken, R. Caracas, F. Detraux, M. Fuchs et al., First-principles computation of material properties: the ABINIT software project, Computational Materials Science, vol.25, issue.3, p.478, 2002.
DOI : 10.1016/S0927-0256(02)00325-7

]. J. Launay, Lattice Dynamics of Body???Centered and Face???Centered Cubic Metallic Elements. II, The Journal of Chemical Physics, vol.22, issue.10, p.1676, 1954.
DOI : 10.1063/1.1739871

H. Andersen, Molecular dynamics simulations at constant pressure and/or temperature, The Journal of Chemical Physics, vol.72, issue.4, p.2384, 1980.
DOI : 10.1063/1.439486

M. Parrinello and A. Rahman, Polymorphic transitions in single crystals: A new molecular dynamics method, Journal of Applied Physics, vol.52, issue.12, p.7182, 1981.
DOI : 10.1063/1.328693

S. Foiles, M. Baskes, and M. Daw, Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys, Physical Review B, vol.33, issue.12, p.7983, 1982.
DOI : 10.1103/PhysRevB.33.7983

M. Daw, S. Foiles, and M. , The embedded-atom method: a review of theory and applications, Materials Science Reports, vol.9, issue.7-8, p.251, 1993.
DOI : 10.1016/0920-2307(93)90001-U

F. Ducastelle and F. Cyrot-lackmann, Moments developments, Journal of Physics and Chemistry of Solids, vol.32, issue.1, p.285, 1971.
DOI : 10.1016/S0022-3697(71)80031-8

URL : https://hal.archives-ouvertes.fr/jpa-00215863

P. Blöchl, O. Jepsen, and O. K. Andersen, Improved tetrahedron method for Brillouin-zone integrations, Physical Review B, vol.49, issue.23, p.16223, 1994.
DOI : 10.1103/PhysRevB.49.16223

H. Monkhorst and J. Pack, Special points for Brillouin-zone integrations, Physical Review B, vol.13, issue.12, p.5188, 1976.
DOI : 10.1103/PhysRevB.13.5188

D. Errandonea, Y. Meng, M. Somayazulu, and D. Häusermann, Pressure-induced transition in titanium metal: a systematic study of the effects of uniaxial stress, Physica B: Condensed Matter, vol.355, issue.1-4, p.116, 2005.
DOI : 10.1016/j.physb.2004.10.030

E. Fisher and D. Dever, Science Technology and Application of titanium (Jaffe R, Promisel NE editors, 1970.

M. Horn, C. Schwerdtfeger, and E. Meagher, Refinement of the structure of anatase at several temperatures*, Zeitschrift f??r Kristallographie, vol.136, issue.3-4, p.273, 1972.
DOI : 10.1524/zkri.1972.136.3-4.273

J. Burdett, T. Hughbanks, G. Miller, J. Richardson, and J. Smith, Structural-electronic relationships in inorganic solids: powder neutron diffraction studies of the rutile and anatase polymorphs of titanium dioxide at 15 and 295 K, Journal of the American Chemical Society, vol.109, issue.12, p.3639, 1987.
DOI : 10.1021/ja00246a021

M. Beg and S. Shapiro, Study of phonon dispersion relations in cuprous oxide by inelastic neutron scattering, Physical Review B, vol.13, issue.4, p.1728, 1976.
DOI : 10.1103/PhysRevB.13.1728

E. Shirley, R. Martin, G. Bachelet, and D. Ceperley, Role of forms of exchange and correlation used in generating pseudopotentials, Physical Review B, vol.42, issue.8, p.5057, 1990.
DOI : 10.1103/PhysRevB.42.5057

M. Fuchs and M. Scheffler, Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory, Computer Physics Communications, vol.119, issue.1, p.67, 1999.
DOI : 10.1016/S0010-4655(98)00201-X

M. Rohlfing, P. Krüger, and J. Pollmann, Quasiparticle Band Structure of CdS, Physical Review Letters, vol.75, issue.19, p.3489, 1995.
DOI : 10.1103/PhysRevLett.75.3489

M. Rohlfing, P. Krüger, and J. Pollmann, electrons in quasiparticle band-structure calculations, Physical Review B, vol.57, issue.11, p.6485, 1998.
DOI : 10.1103/PhysRevB.57.6485

D. Vogel, P. Krüger, and J. Pollmann, Self-interaction and relaxation-corrected pseudopotentials for II-VI semiconductors, Physical Review B, vol.54, issue.8, p.5495, 1996.
DOI : 10.1103/PhysRevB.54.5495

A. Svane and O. Gunnarsson, Transition-metal oxides in the self-interaction???corrected density-functional formalism, Physical Review Letters, vol.65, issue.9, p.1148, 1990.
DOI : 10.1103/PhysRevLett.65.1148

M. Arai and T. Fujiwara, Electronic structures of transition-metal mono-oxides in the self-interaction-corrected local-spin-density approximation, Physical Review B, vol.51, issue.3, p.1477, 1995.
DOI : 10.1103/PhysRevB.51.1477

S. Goedecker and C. Umrigar, Critical assessment of the self-interaction-corrected???local-density-functional method and its algorithmic implementation, Physical Review A, vol.55, issue.3, p.1765, 1985.
DOI : 10.1103/PhysRevA.55.1765

M. Biagani, Self-interaction-corrected density-functional formalism, Physical Review B, vol.49, issue.3, p.2156, 1994.
DOI : 10.1103/PhysRevB.49.2156

]. R. Heaton, J. Harrison, and C. Lin, Self-interaction correction for density-functional theory of electronic energy bands of solids, Physical Review B, vol.28, issue.10, p.5992, 1983.
DOI : 10.1103/PhysRevB.28.5992

]. D. Vogel, P. Krüger, and J. Pollmann, Structural and electronic properties of group-III nitrides, Physical Review B, vol.55, issue.19, p.12836, 1997.
DOI : 10.1103/PhysRevB.55.12836

D. Vogel, P. Krüger, and J. Pollmann, electronic structure of silver halides calculated with self-interaction and relaxation-corrected pseudopotentials, Physical Review B, vol.58, issue.7, p.3865, 1998.
DOI : 10.1103/PhysRevB.58.3865

P. Daosta, O. Nielsen, and K. Kunc, Stress theorem in the determination of static equilibrium by the density functional method, Journal of Physics C: Solid State Physics, vol.19, issue.17, p.3163, 1986.
DOI : 10.1088/0022-3719/19/17/012

C. Stassis, D. Arch, B. Harmon, and N. Wakabayashi, Lattice dynamics of hcp Ti, Physical Review B, vol.19, issue.1, p.181, 1979.
DOI : 10.1103/PhysRevB.19.181

W. Petry, A. Heiming, J. Trampenau, M. Alba, C. Herzig et al., Phonon dispersion of the bcc phase of group-IV metals. I. bcc titanium, Physical Review B, vol.43, issue.13, p.10933, 1991.
DOI : 10.1103/PhysRevB.43.10933

K. Persson and M. Ekman, Phonon instabilities in bcc Sc, Ti, La, and Hf, Physical Review B, vol.61, issue.17, p.11221, 2000.
DOI : 10.1103/PhysRevB.61.11221

H. Ledbetter, H. Ogi, S. Kai, S. Kim, and M. Hirao, Elastic constants of body-centered-cubic titanium monocrystals, Journal of Applied Physics, vol.95, issue.9, p.4642, 2004.
DOI : 10.1063/1.1688445

D. Trinkle, M. Jones, R. Hennig, S. Rudin, R. Albers et al., Empirical tight-binding model for titanium phase transformations, Physical Review B, vol.73, issue.9, p.94123, 2006.
DOI : 10.1103/PhysRevB.73.094123

URL : http://arxiv.org/abs/cond-mat/0502636

P. Pavone, S. Baroni, and S. Gironcoli, ??????? phase transition in tin: A theoretical study based on density-functional perturbation theory, Physical Review B, vol.57, issue.17, p.10421, 1998.
DOI : 10.1103/PhysRevB.57.10421

M. Yin and M. Cohen, Structural theory of graphite and graphitic silicon, Physical Review B, vol.29, issue.12, p.6996, 1984.
DOI : 10.1103/PhysRevB.29.6996

M. Aven, R. Craig, T. Waite, and W. Wallace, Heat Capacity of Titanium between 4??K and 15??K, Physical Review, vol.102, issue.5, p.1263, 1956.
DOI : 10.1103/PhysRev.102.1263

W. Corak and C. Satterhwaite, Atomic Heats of Normal and Superconducting Tin between 1.2?? and 4.5??K, Physical Review, vol.102, issue.3, p.662, 1956.
DOI : 10.1103/PhysRev.102.662

F. Willaime and C. Massobrio, -body interatomic potential for hcp and bcc zirconium, Physical Review B, vol.43, issue.14, p.11653, 1991.
DOI : 10.1103/PhysRevB.43.11653

URL : https://hal.archives-ouvertes.fr/halshs-00309957

F. Willaime and C. Massobrio, -body potential, Physical Review Letters, vol.63, issue.20, p.2244, 1989.
DOI : 10.1103/PhysRevLett.63.2244

URL : https://hal.archives-ouvertes.fr/halshs-00309957

R. Willens, Vacuum X???Ray Diffractometer for High Temperature Studies of Metals Sensitive to Contamination by Oxygen and Nitrogen, Review of Scientific Instruments, vol.33, issue.10, p.1069, 1962.
DOI : 10.1063/1.1717685

S. Liu, C. Stassis, and K. Ho, Origin of the zone-center [001] LO-phonon anomaly in superconducting hcp transition metals, Physical Review B, vol.24, issue.9, p.5093, 1981.
DOI : 10.1103/PhysRevB.24.5093

A. Becke, Density???functional thermochemistry. III. The role of exact exchange, The Journal of Chemical Physics, vol.98, issue.7, p.5648, 1993.
DOI : 10.1063/1.464913

C. Cousins and J. Phys, C : Solid State Phys, p.4881, 1978.

G. B. Grad, P. Blaha, J. Luitz, K. Schwarz, A. F. Guillermet et al., study of Y, Zr, Nb, and Mo, Physical Review B, vol.62, issue.19, p.12743, 2000.
DOI : 10.1103/PhysRevB.62.12743

S. A. Ostanin and V. Y. Trubitsyn, First-principles investigation of the phase stability of zirconium, Physics of the Solid State, vol.39, issue.11, p.1727, 1997.
DOI : 10.1134/1.1130158

E. G. Moroni, G. Grimvall, and T. Jarlborg, Free Energy Contributions to the hcp-bcc Transformation in Transition Metals, Physical Review Letters, vol.76, issue.15, p.2758, 1996.
DOI : 10.1103/PhysRevLett.76.2758

A. Heiming, W. Petry, J. Trampenau, M. Alba, C. Herzig et al., Phonon dispersion of the bcc phase of group-IV metals. II. bcc zirconium, a model case of dynamical precursors of martensitic transitions, Physical Review B, vol.43, issue.13, p.10948, 1991.
DOI : 10.1103/PhysRevB.43.10948

J. Goldak, L. T. , and C. S. Barrett, Lattice Parameters, Thermal Expansions, and Gr??neisen Coefficients of Zirconium, 4.2 to 1130??K, Physical Review, vol.144, issue.2, p.478, 1966.
DOI : 10.1103/PhysRev.144.478

H. Xia, S. J. Duclos, A. L. Ruoff, and Y. K. Vohra, New high-pressure phase transition in zirconium metal, Physical Review Letters, vol.64, issue.2, p.204, 1990.
DOI : 10.1103/PhysRevLett.64.204

D. Wallace, Thermodynamics of Crystals, American Journal of Physics, vol.40, issue.11, 1972.
DOI : 10.1119/1.1987046

D. Wallace, Statistical physics of crystals and liquids, World Scientific, 2002.
DOI : 10.1142/5060